No, when you click on a forum on the bottom there is a box (next to the who's on the forum) with "modderators" in which stands " Usergroup Chat Moderators , Usergroup Forum Moderators " and the counter was at 8.
Technically, the "Chat Moderators" do have the ability to moderate the forum, but only in one very specific way. They can approve/reject posts by moderated people.
This ability is given to them so that people who fall into moderated status through low rep can get their posts reviewed more promptly.
Annoyingly, some of the code I've recently imported has decided to override my previously-configured settings and start displaying the details of moderators when browsing inside forums. I'll see about curtailing this.